And there are further similarities: The streets of New York look beautiful (not just Manhattan — we’re talking Brooklyn.) The cinematography is meticulous. There are some fabulous apartments. And there’s that multi-talented cast of actors you’d never think of together: Sharon Stone and Sofia Vergara? Vanessa Paradis and Liev Schreiber?

But “Fading Gigolo” isn’t a Woody Allen film — it’s a John Turturro film, with a rare acting-only appearance by Allen. And it’s a credit to Turturro — who writes, directs and stars — that despite all these initial parallels, it ends up feeling like his movie, going in directions you don’t expect.

That’s both a compliment and a criticism. The movie feels like several films combined. On one level, it’s slapstick comedy, particularly when Allen rips off those one-liners. On another, it’s a much deeper meditation on loneliness and the need for connection. Oh, and on the strictures of religion, too. The various tones don’t always mesh harmoniously.

But we’ll take messy and interesting over neat and uninteresting any day — especially when a movie has as much heart as this.

The plot is unabashedly preposterous. Murray (that would be Allen) owns a failing rare book shop. As he’s sadly packing to close down, he mentions to his friend Fioravante (Turturro), a quiet book-lover and part-time florist, that his dermatologist told him she’s looking for a man to participate in a minage a trois with her and her best friend. Does Murray have any suggestions?

If you think that’s unlikely — that your dermatologist would ask you to set up a threesome — let’s add that the dermatologist is Sharon Stone, an actress who gets even better-looking as she ages. And her friend? Sofia Vergara. And they’re offering a cool thousand.

For economic reasons, Fioravante gives in, and in his first meeting with the bombshell doctor, sweeps her off her feet, showing you men out there (women already know this) that you don’t need to be good-looking to be sexy — just confident, thoughtful and truly interested in what a woman has to say.

Suddenly, a business is born. Murray is the pimp. Fioravante is the “ho.” And everyone’s pretty happy.

Then the movie shifts gears. Murray takes the children he looks after (too complicated to explain here) to get their hair de-loused by a Hasidic Jewish woman in Williamsburg, Avigal (a surprisingly wonderful Paradis), the young widow of a much older rabbi. Her religion dictates that her hair must be covered and her skin, too, from neck to knees.

And yet Murray thinks she could be a good client for Fioravante. Inappropriate as this sounds, Fioravante handles the situation with grace. Somehow the two, when they meet, fill a crucial need in each other’s lives. Their scenes together are quite touching, particularly a slow lunch in which Avigal shows Fioravante how to debone a fish.

Their budding relationship, though, causes angst for Dovi (Schreiber, also excellent), a Hasidic man who secretly pines for Avigal. A suspicious type, he also serves on a neighborhood auxiliary police force, which makes it easy for him to spy on Avigal.

All of which gets Murray into some real trouble. And here the film veers quickly back into slapstick mode. For a bit, anyway. It ends on a bittersweet but appealing note. And then you realize that you’ve been thoroughly moved, by a movie about a morose florist-gigolo and his wise-cracking book-dealer pimp.

That’s what’s fun about the movies, isn’t it?

“Fading Gigolo,” a Millennium Entertainment release, is rated R by the Motion Picture Association of America “for some sexual content, language and brief nudity.” Running time: 90 minutes. Three stars out of four.